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Search: id:A160238
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| A160238 |
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Numbers n such that n^2 can be expressed as the sum of three different Fibonacci numbers. |
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1
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| 3, 5, 7, 8, 9, 10, 16, 17, 18, 20, 23, 24, 25, 32, 33, 35, 37, 47, 57, 86, 112, 123, 139, 216, 322, 843, 1161, 1476, 2207, 4999, 5778, 15127, 39603, 103682, 271443, 710647, 1860498, 4870847, 12752043
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OFFSET
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1,1
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COMMENT
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There exist a proper subsequence b(i)of a(n): n=[1, 2, 8, 17, 21, 24, 25, 28,29, 30, 31, 32, 33, 34, ...] such that approximatively b(i+1)=b(i)*(1+phi) where phi is 1.618... is the golden ratio and the approximation holds as a limit when i goes to infinity. For such a subsequence b(i) we have the following formula for the corresponding term when squared b(i)*b(i)=Fib(4*i+1)+Fib(4*i-1)+Fib(3). In the previous example 4999=b(9).
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EXAMPLE
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4999*4999=24990001=Fib(37)+Fib(35)+Fib(3)
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CROSSREFS
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A000045
Sequence in context: A047746 A111638 A080262 this_sequence A025050 A025051 A020884
Adjacent sequences: A160235 A160236 A160237 this_sequence A160239 A160240 A160241
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KEYWORD
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nonn
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AUTHOR
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Carmine Suriano (surianonoi5(AT)libero.it), May 05 2009
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